- Sputnik I, launched by the Soviet Union
December 03, 2020
Space Shuttle Challenger exploded moments after launching on January 28, 1986. Source: CNN news
Source: https://www.kaggle.com/agirlcoding/all-space-missions-from-1957
Logistic Regression \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1} + \beta_2 X_{2} + \ldots + \beta_k X_{k}\]
Binary categorical response variable (yes-no, pass-fail, success-failure, etc.)
Single Logistic Regression models \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X\]
Response variable: Mission Outcome (Success: Yes/No)
Predictors: Rocket Status (Active/Retired), Country (USA/Russia), Space Race Decade (1960s/1970s)
Inferences for the slope term:
\[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X\]
Odds of observing a success when \(X = 0\) (reference category): \(e^{\beta_0}\)
Odds of observing a success when \(X = 1\) (indicated category): \(e^{\beta_0 + \beta_1} = e^{\beta_0} e^{\beta_1}\)
Odds ratio = \(e^{\beta_1}\)
Interpretation: odds of a success occurring when \(X = 1\) is OR times greater than when \(X = 0\).